Our experimental assembly consists of a large main volume and a smaller sinter-filled heat-exchanger volume connected together by a narrow channel. Most of the main volume is filled with saturated 3 He-4 He mixture at its crystallization pressure together with solid pure 4 He, while the top of the main volume, the connecting channel, and the sinter volume are filled with liquid pure 3 He. The liquid phases in the main volume are monitored by two quartz tuning fork resonators. The system is cooled externally by a copper nuclear demagnetization stage, and, as an option, internally by the adiabatic melting of solid 4 He in the cell. Thermal behavior of this system gives rich information upon the thermal conductivity of 3 He in the connecting channel, as well as the Kapitza resistance between liquid helium and the plain cell wall in the main volume, and between liquid and the sinter in the heat-exchanger volume. None of those components are well-known apriori at 1 mK temperature range. In particular, the available thermal conductivity data of pure superfuid 3 He is very limited.